Concept Of Integer Research Articles

“Awur Eser” to Explore Number Sense: Hypothetical Learning Trajectory for Integer Material Facilitating Learning Speed

This article aims to explore the concept of "Awur Eser" as a potential learning method to enhance students' number sense, especially in the context of learning integer concepts, and to develop more effective and inclusive strategies for mathematics education. We conducted a literature review to identify students’ barriers to understanding integers based on their number sense and learning speed. Then, we conducted a second literature review to design a Hypothetical Learning Trajectory (HLT) for integer learning. Subsequently, we held a Focus Group Discussion (FGD) with mathematics education experts and teachers to discuss and validate the selection of HLT for integer learning. Based on the FGD results, we compiled the final design of HLT for integer learning. This design involves adjustments based on input from experts and teachers, ensuring alignment with students' characteristics and needs. The implementation of HLT hopefully can improve students' conceptual understanding and accelerate the learning process.

THE EFFECTIVENESS OF MATHEMATICS LEARNING THROUGH A REALISTIC MATHEMATICS EDUCATION APPROACH IN ELEMENTARY SCHOOLS

The research aims to analyze the effectiveness of mathematics learning through the realistic mathematics education approach in learning the concept of counting integers in grade VI elementary school students. The research used a quasi-experiment with one pretest postets design. The research involved 32 grade VI students at SDN 205 Neglasari, Coblong District, Bandung City. The research instrument is in the form of a multiple-choice test that includes addition and subtraction of decimal numbers. Research shows that the RME approach is effective in producing a significant improvement in students' learning completeness in the addition and subtraction of decimal integers, as well as improving mathematical problem-solving, self-efficacy, reasoning, and mathematical literacy. RME encourages students to recognize the practical application of mathematical concepts through real-world contexts and cultural elements, as well as to cultivate creative and imaginative thinking skills so that they can be an important strategy in improving mathematics education in primary schools.

Identification of the Difficulties of Middle School Students in Understanding the Mixed Operations of Integer

The difference between the students’ conceptions and the conceptual substance has led to a misconception regarding the mixed arithmetic operation on integers. This study aims to describe students’ understanding and to identify learning difficulties related to the mixed operation of integers. This study was a qualitative study with a case study design. The subjects of the study were the students of grade VII of a junior high school in Bandung. The data collection was done through tests, interviews, and curriculum documents. Data analysis is descriptive in general by reposing data, presenting data, and drawing conclusions. From the results of the study, it can be concluded that students have difficulties in understanding the concept of integers and their operation, especially those related to the mixed operations of integers. Based on the data analysis, it can be shown that some students recognize numbers only as a formal symbol in mathematics. Numbers for them are something abstract so they have difficulty when they present these numbers in concrete. Another result is students have difficulty in using mixed operations of integers. Keywords: difficulties of middle school students, mixed operations of integer, understanding

Transitional-Apprehending Mental Model for Junior High School Students in Understanding the Concept of Integers

Transitional-Apprehending Mental Model for Junior High School Students in Understanding the Concept of Integers

STUDI KOMPARASI PENGGUNAAN MULTIMEDIA POWERPOINT DAN VIDEO ANIMASI DALAM MENINGKATKAN PEMAHAMAN KONSEP BILANGAN BULAT PADA SISWA SMP

This study aims to compare the use of PowerPoint multimedia and video animation in improving the understanding of integer concepts in junior high school students. The use of interactive multimedia is an important part of education today, but the use of multimedia is still limited when teaching in the classroom. In this research, an experiment was carried out involving two groups of junior high school students. The first group used animated videos while the second group used PowerPoint multimedia. The data collected includes tests of understanding the concept of integers before and after using PowerPoint multimedia and animated videos in teaching. The analysis used includes the normality test, homogeneity test, and t-test to test whether there is a difference or not from the data of each group. The results of the data analysis show that there are differences in understanding the concept of concept numbers between those using powerpoint media and animated videos. The group that experienced the most significant difference was the group that used video animation compared to the group that used PowerPoint multimedia. The use of animated videos in this context can be an effective and interesting alternative in learning the context of integers.

Analisis Pemahaman Konsep Siswa Kelas 4 pada Materi Bilangan Bulat di Sekolah Dasar

This study examined how well fourth-grade children understood the concepts related to the integer material taught to elementary school students. A descriptive study employing a concept understanding test instrument was used as the research methodology. Three pupils in grade 4 mad e up the study sample. Data was gathered using a written test that was given to the pupils and covered basic school-level topics on integers. The analysis's findings indicate that many pupils struggle to comprehend the idea of integers, particularly the concepts of positive and negative numbers as well as integer multiplication and division operations. Ineffective teaching strategies, a lack of practice, and individual student characteristics like curiosity and willingness to study are all factors that hinder student comprehension. In order to improve students' comprehension of integer concepts, teachers can devise engaging, engaging, and active learning strategies. They can also provide students with more intensive practice and enrichment of pertinent material, pay attention to individual student factors, and promote positive learning interest and motivation. This study offers guidance to primary school instructors and administrators on how to improve their students' comprehension of integer concepts. Additionally, this study can serve as a springboard for future studies aimed at creating more efficient learning methods for complicated mathematical materials.

ETNOMATEMATIKA PADA KUE KHAS ACEH SEBAGAI BAHAN PEMBELAJARAN MATEMATIKA

Ethnomathematics is a study of mathematics that implements culture in the teaching and learning process, especially in mathematics learning, can be an alternative in teaching mathematics and also introduces cultural values to students, especially in Acehnese cake culture. Most students do not realize that in everyday life they have applied mathematical concepts. This is because students only consider that mathematical concepts are only learned during mathematics subjects at school. This study aims to describe the ethnomathematics found in typical Acehnese cakes. This type of research is qualitative research with an ethnographic approach. The data collection method is observation conducted by 5 observers, interviews with 5 typical Acehnese cake makers, and documentation. The results showed that there is ethnomathematics in typical Acehnese cakes, namely being a medium for learning mathematics about the concepts of integers, fractions, awakening and congruence, building flat, and building space

Examining the Effect of Elementary School 5th Grade Subject of Extraction on Readiness for Integers

The concept of number sense first appeared theoretically in the report published by NCTM in 1989. Although it is an important concept that includes the meaning of numbers and the relationship between numbers, it is very difficult to make a clear definition of it. This could also be true for the concept of integer, which we cannot place in our world of meaning in daily life or which we have difficulty in finding an equivalent for. For integers that have an abstract world of meaning, a misconception may occur between the integer sign and the sign used for operation. In this respect, this study aimed to examine the effect of subtraction, which can create pre-learning, on the concept of integers. Moreover, it was requested to demonstrate that the operational knowledge used by students in subtraction can be utilized in teaching integers. A total of 17 students studying in the 5th grade of a secondary school in Turkey participated in the study. As the research design, the action research method, one of qualitative research methods, was used, and the data were collected with the trilogy technique. The data obtained were analyzed using descriptive analysis and content analysis. The findings revealed that the teaching technique of subtraction opened the door for students to form and make sense of the concept of minus. In this context, it is recommended to provide mathematical skills in a cumulative manner.

Eksplorasi Etnomatematika pada Permainan Tradisional Bekles

The purpose of this study is to explore the ethnomathematical values ​​contained in traditional games in West Java, namely bekles or beklen. This study uses an ethnographic research design with a qualitative research approach. The object of this research is the rules of the game and the object of the game itself. The research subjects were two resource persons consisting of 1 child aged 8 years and 1 teenager aged 13 years. This research is located on Jl. Raden Soleh, RT 01 RW 05 Sindangsari Village, Kec. Kadupandak, Kab. Cianjur, West Java. Data was collected by using the methods of documentation, interviews, and observations. The results of this study indicate that there are ethnomathematical values ​​contained in traditional bekles games, namely the concept of integers from 1 to 10, the concept of modulu or remainder of division, the shape of the ball space, and probability. In addition, it can also be used as a problem in learning physics about the material of upper vertical motion and free fall motion. Based on the research results, it is known that the potential for ethnomathematics development in traditional bekles games is very large, which can be used as materials, teaching materials, or learning media such as student worksheets (LKPD).

The awareness of difficulties in solving rational inequality and a solution proposal

This research aimed to determine the difficulties that the students experience in inequality solutions that contain inequality in general and rational (proportional) expressions, and to solve these difficulties with an activity. Totally 108 students, who were enrolled in the Department of Mathematics and Science Education, consisted respectively of 43 in the 2015-2016, 32 in the 2016-2017, and 33 in the 2017-2018 academic year, participated in the research. It was started with an activity to make students realize the difficulties they experienced and become aware of the stages which they had difficulty. After the activity, the difficulties, and the stages that students had difficulties were determined. At that point, they were informed about the solutions for the difficulties they faced and shown a road map for coping with the stages they had difficulties. At the end of the research, the rational inequality questions were asked to the students in the mid-term and/or final exams, and it was observed that the majority of students did not experience any of the problems which they had experienced before the activity. Another result of the study was that the students had less difficulty in the inequalities related to the concept of greatest integer, which they received only in university education.

Analisis Kesulitan Peserta Didik Dalam Menyelesaikan Soal Bilangan Bulat Kelas VII SMPN 3 Kota Solok

This research is motivated by the difficulties experienced by students in solving integer problems. The purpose of this study is to describe the difficulties of students in solving integer problems for class VII SMPN 3 Solok City and to describe what factors cause students' difficulties in solving integer problems for class VII SMPN 3 Solok City. The research method used in this research is the descriptive method. The subjects of this study were students of class VII.1 SMPN 3 Solok City, totaling 29 people. Data was collected by using test and interview techniques. Based on data analysis, it can be concluded that most students have difficulty understanding concepts, applying facts, and stages of procedures/skills on integer questions. The factors that cause students' difficulties in solving integer problems are 1) The inability of students to perform arithmetic operations, 2) Students are lazy to describe the steps in solving problems, 3) Lack of understanding of students about the concept of negative integers and positive integers, 4) Students do not re-examine the results of their work, 5) Lack of self-confidence of students, 6) Rarely practice integer questions in their spare time, 7) Students do not take the questions seriously.

The Development Of Two Room Board Media With Ilustrated Story Boards Based On Realistic Mathematics On Integers Through Blended Learning Strategies

Blended learning as a combination of synchronous and asynchronous learning is a limited face-to-face learning solution in the current pandemic era. For this reason, the authors develop two-space boards interactive media to facilitate students learning integers material with realistic math-based illustrated story books. The development uses a 4D model from Tiagarajan (1974) which consists of four steps: define, design, develop, and disseminate. Through a blended learning strategy that provides opportunities for students to interact with a two-room board media combined with realistic math-based illustrated story books about the application of integers, it is hoped that students will be able to understand the concept of integers better. This teaching aid was tested on sixth grade students of SDN Jenang 02 Academic on 2021/2022. The result is that the use of a two-room board combined with a picture story book about the application of integer arithmetic operations in everyday life can improve understanding of the concept of counting integers, and the integration of its use with question cards can improve students' skills in arithmetic operations of addition and subtraction of integers.

ANALYSIS OF STUDENT'S ABILITY IN COMPLETING OPERATIONS OF SUMMARY AND REDUCTION OF INTEGER NUMBERS

This study aims to describe the abilities and difficulties experienced by students in solving arithmetic operations on addition and subtraction of integers in SDIT Bunayya class. The data was collected by using test, interview, observation, and documentation methods. From the interview data, it shows that in solving problems students do not understand the concept of addition and subtraction of integers, the factor causing the difficulties experienced by students in solving problems is the lack of willingness to learn from within students. Students are often lazy to learn mathematics, do not want to listen to the teacher's explanation when the lesson is in progress, students do not concentrate fully during teaching and learning activities, students are afraid to ask the teacher if they do not understand the material. The material being taught, students always assume that mathematics is very difficult, students are less careful when working on problems. The results showed that the learning activities facilitated by the teacher were included in the good category. The teacher presents the lesson in an interesting way so that the learning process is not boring. The discussion method is used during the learning process to encourage students to ask questions and discuss so that students can share ideas. Students have difficulty solving problems between positive integers and negative integers in the form of stories. Students have difficulty because students do not understand the concept of integers contextually. This can be overcome by using learning media and contextual emphasis on learning concepts and observing student development using the results of the evaluation at the end of the class.

Students' Understanding of the Integer Concept in Terms of Ethno-Mathematical Experience in a Traditional Marbles Game

The goal of this qualitative study was to examine students’ understanding of the integer concept in terms of ethno-mathematical experiences in a traditional marbles game. A total sample of 54 students was selected from a population of 63 grade VII students at SMP Negeri 30 Konawe Selatan using simple random sampling techniques. Observations, questionnaires and test descriptions were used as data collection techniques. The data were analyzed descriptively. The findings revealed that the majority of students consciously and unconsciously applied mathematical concepts to the marbles game. Even though the average score did not meet the minimum completeness criteria, students who never implemented the concept had a higher average score of concept understanding than students who implemented it. When examining the percentages of concept understanding based on ethno-mathematical experience, students in the good, sufficient and poor categories understood the integer concept at 33.93%, 37.59% and 41.07%, respectively. Students with a low level of ethno-mathematical experience had a higher average understanding of concepts than students with a high / good level of ethno-mathematical experience, according to the findings.
 Keywords: concept of integers, ethnomatematic experience, traditional marbles game, mathematics

The Learning Trajectory Construction of Elementary School Students in Solving Integer Word Problems

The integer is a basic concept in studying arithmetic and algebra. However, students still frequently experience misconceptions, especially in negative integer, count operations. Traditional games are activities that are often carried out by students in coastal areas so that they are relevant to be used as a tool to construct learning trajectories in solving integer word problems. The aim of this study is to produce a learning trajectory that can be used to solve integer word problems using traditional games. This study used a design-based research. Participants in this study were five grade sixth elementary school students. There are 6 sub-topics studied, i.e., the concept of negative integers, sequence integers, addition and subtraction operations, division and multiplication operations, mixed count operations, and solving problems related to integers. The results of this study obtained student learning trajectories for each sub-topic including the free play, collecting data from the game results, making mathematical relationships, building concepts, and applying them to various problems. Students are able to do problem-solving based on the sequence of tasks but require intervention so they can apply it to other situations without engaging in activities. Further research is required for more in-depth exploration on thinking process, instruction types, and behaviours that students might display independently without using traditional games in solving integer word problems.

Model mental transition-attempting: The case of beginners students in understanding the concept of integers

Model mental transition-attempting: The case of beginners students in understanding the concept of integers

Assessing The Characteristics of Elementary School Students' Mental Models in Understanding The Concept of Integers

This study aims to reveal the characteristics of the mental model of elementary school students in understanding the concept of integers. The subjects in this study were selected based on outlier criteria or unique responses to a series of tests given to 30 students of the third grade of elementary school. As a result, two students were chosen as research subjects. The research data were collected through observation and interviews. Observation made by the researchers were direct observations, in which the researchers see and observe the activities of students in doing the test. In addition, the researchers also conducted interviews with research subjects. The results of the students' works were reviewed, and then interviews were conducted to clarify the students' answers. The results showed that the characteristics of elementary school students in understanding integers did not always move from the synthetic stage to the formal stage, but there were lower grade students who were able to solve contextual problems related to integers. The process of forming students' formal mental models can be seen when they solve the temperature rise problem by counting fingers and comparing them with the zero symmetry position between negative and positive integers.

CONGKLAK APLICATION TO INCREASE UNDERSTANDING THE CONCEPT OF ROUND NUMBERS IN ELEMENTARY SCHOOLS

The purpose of this study was to determine students' understanding of integer concepts through innovative learning media.The method used in this research is Research and Development (R and D) research to produce a product.The Congklak application is designed by incorporating the traditional congklak game. This research was conducted at SD Negeri Sayung 1, Sayung District, Demak Regency. The product is designed through learning integer material using the context of the congklak game. The research stage consists of information gathering, planning, product development and product validation.The results of this study indicate that the Congklak application (Congklak.App) can be used to improve understanding of the integer concept. This is supported by the results of teacher and student responses as well as the results of the validation of experts showing very good criteria and suitable for use in learning integer concepts in elementary schools.

Bootstrapping of integer concepts: the stronger deviant-interpretation challenge (and how to solve it)

Beck (Cognition 158:110–121, 2017) presents an outline of the procedure of bootstrapping of integer concepts, with the purpose of explicating the account of Carey (The Origin of Concepts, 2009). According to that theory, integer concepts are acquired through a process of inductive and analogous reasoning based on the object tracking system (OTS), which allows individuating objects in a parallel fashion. Discussing the bootstrapping theory, Beck dismisses what he calls the "deviant-interpretation challenge"—the possibility that the bootstrapped integer sequence does not follow a linear progression after some point—as being general to any account of inductive learning. While the account of Carey and Beck focuses on the OTS, in this paper I want to reconsider the importance of another empirically well-established cognitive core system for treating numerosities, namely the approximate number system (ANS). Since the ANS-based account offers a potential alternative for integer concept acquisition, I show that it provides a good reason to revisit the deviant-interpretation challenge. Finally, I will present a hybrid OTS-ANS model as the foundation of integer concept acquisition and the framework of enculturation as a solution to the challenge.

Meeting the Needs of Malaysian Mathematically Talented Students by An Enrichment Program: A Module For Primary School Students

School holiday enrichment program annually organized by PERMATApintar National Gifted Centre was to uncover hidden talents in science and mathematics. Students in this program were grouped into different courses. In order to run the Introduction to Cryptology course for primary school students, a new module has been developed. This module has been implemented for the first time during the school holiday program in December 2017. Thus, this study aimed at determining mathematics achievement of 34 Malaysian primary school students in Introduction to Cryptology course. An examination consisting of a set of questions on mathematical concepts was being given to each of the students during the final day of the program. Student scores were being evaluated to assess their achievement. Findings indicate that 73.6% of students scored between 80 and 100 in the examination. Students have good achievement in the concept of integers but they have deficiency in the concept of matrices. Hence, it can be concluded that the students indeed have special ability in doing mathematics. Since matrices were new to Malaysian primary school students, thus interesting activities relating to matrices will be included in the module to intensify students’ motivation in mathematics.